The cauchy problem for the Euler equations for compressible fluids

Some recent developments in the study of the Cauchy problem for the Euler equations for compressible fluids are reviewed. The local and global well-posedness for smooth solutions is presented, and the formation of singularity is exhibited; then the local and global well-posedness for discontinuous solutions, including the BV theory and the L∞ theory, is extensively discussed. Some recent developments in the study of the Euler equations with source terms are also reviewed. © 2002 Elsevier B.V. All rights reserved.